Upper mantle seismic anisotropy at a strike-slip
boundary: South Island, New Zealand
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Citation
Zietlow, Daniel W., Anne F. Sheehan, Peter H. Molnar, Martha K.
Savage, Greg Hirth, John A. Collins, and Bradford H. Hager.
“Upper Mantle Seismic Anisotropy at a Strike-Slip Boundary:
South Island, New Zealand.” Journal of Geophysical Research:
Solid Earth 119, no. 2 (February 2014): 1020–1040. © 2013
American Geophysical Union
As Published
http://dx.doi.org/10.1002/2013JB010676
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Journal of Geophysical Research: Solid Earth
RESEARCH ARTICLE
10.1002/2013JB010676
Key Points:
• Shear wave splitting measurements
are made on and offshore South
Island, NZ
• Strong anisotropy spans a zone 100200 km on each side of Alpine fault
• Both thin viscous sheet and
asthenospheric models match
observed anisotropy
Correspondence to:
D. W. Zietlow,
daniel.zietlow@colorado.edu
Citation:
Zietlow, D. W., A. F. Sheehan, P. H.
Molnar, M. K. Savage, G. Hirth, J. A.
Collins, and B. H. Hager (2014), Upper
mantle seismic anisotropy at a strikeslip boundary: South Island, New
Zealand, J. Geophys. Res. Solid Earth,
119, 1020–1040, doi:10.1002/
2013JB010676.
Received 6 SEP 2013
Accepted 20 DEC 2013
Accepted article online 28 DEC 2013
Published online 5 FEB 2014
Upper mantle seismic anisotropy at a strike-slip
boundary: South Island, New Zealand
Daniel W. Zietlow1, Anne F. Sheehan1, Peter H. Molnar1, Martha K. Savage2, Greg Hirth3,
John A. Collins4, and Bradford H. Hager5
1
CIRES and Department of Geological Sciences, University of Colorado Boulder, Boulder, Colorado, USA, 2Institute of
Geophysics, Victoria University of Wellington, Wellington, New Zealand, 3Department of Geological Sciences, Brown
University, Providence, Rhode Island, USA, 4Department of Geology and Geophysics, Woods Hole Oceanographic
Institution, Woods Hole, Massachusetts, USA, 5Department of Earth, Atmospheric and Planetary Sciences, Massachusetts
Institute of Technology, Cambridge, Massachusetts, USA
Abstract
New shear wave splitting measurements made from stations onshore and offshore the South
Island of New Zealand show a zone of anisotropy 100–200 km wide. Measurements in central South Island
and up to approximately 100 km offshore from the west coast yield orientations of the fast quasi-shear wave
nearly parallel to relative plate motion, with increased obliquity to this orientation observed farther from shore.
On the eastern side of the island, fast orientations rotate counterclockwise to become nearly perpendicular to
the orientation of relative plate motion approximately 200 km off the east coast. Uniform delay times between
the fast and slow quasi-shear waves of nearly 2.0 s onshore continue to stations approximately 100 km off the
west coast, after which they decrease to ~1 s at 200 km. Stations more than ~300 km from the west coast
show little to no splitting. East coast stations have delay times around 1 s. Simple strain fields calculated
from a thin viscous sheet model (representing distributed lithospheric deformation) with strain rates
decreasing exponentially to both the northwest and southeast with e-folding dimensions of 25–35 km
(approximately 75% of the deformation within a zone 100–140 km wide) match orientations and amounts
of observed splitting. A model of deformation localized in the lithosphere and then spreading out in the
asthenosphere also yields predictions consistent with observed splitting if, at depths of 100–130 km below
the lithosphere, typical grain sizes are ~ 6–7 mm.
1. Introduction
Measurements of seismic anisotropy arguably offer the best way to constrain deformation deep in the Earth’s
subsurface [e.g., Silver, 1996]. With such measurements, it becomes possible to describe the distribution of
strain in the mantle lithosphere (used here to include the relatively strong layer at temperatures less than
around 1200°C), as well as the underlying asthenosphere, in active tectonic regions such as strike-slip zones.
Specifically, does the lithosphere deform continuously over a broad region on the order of hundreds of
kilometers, or is lithospheric deformation localized within a few kilometers around a fault that penetrates the
lithosphere, with more diffuse shear spreading out within the underlying asthenosphere?
The South Island of New Zealand offers an ideal location to investigate subsurface deformation in a strike-slip
zone. The tectonic history of the region is known and relatively simple (Figure 1). Plate reconstructions
indicate ~850 km of displacement between the plates over the past 45 Ma [Sutherland, 1999; Cande and Stock,
2004]. The Alpine fault, a predominately dextral strike-slip fault running the length of the South Island and the
major tectonic feature of the central portion of the South Island, has accommodated approximately 460 km
of this displacement since 45 Ma [e.g., Sutherland et al., 2000]. Over this time period, the relative motion between the Australian and Pacific plates changed little, though a component of convergence initiated around
11 Ma [Cande and Stock, 2004]. This convergence resulted in approximately 100 km of shortening across the
South Island [Walcott, 1998] and the creation of the Southern Alps. Today, geodetic measurements show that
the present plate motion is resolved into approximately 36–39 mm/yr parallel and between 9 and 12 mm/yr
perpendicular to the Southern Alps [Beavan et al., 1999].
Within the South Island, the style of deformation varies from north to south. Northeast of the South Island,
westward subduction of the Pacific plate beneath the Australian plate occurs at the Hikurangi Trough,
becoming increasingly oblique toward the south. This oblique convergence continues under the northern
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Figure 1. Map of New Zealand and surrounding region showing the location of major tectonic features. Also shown is a summary of previous
teleseismic SKS splitting measurements made by Klosko et al. [1999] (blue bars) and by Duclos et al. [2005] (red bars). Black crosses indicate null
measurements, with the orientation showing the two possible fast orientations. Lines through stations show orientations of polarization of the
faster quasi-shear waves. Lengths of lines are proportional to delay times. Inverted yellow triangles represent the locations of ocean bottom
seismometers deployed in the MOANA experiment, and green triangles represent the stations of the New Zealand National Seismograph
Network used in this study. Thick black arrows show current absolute plate motion of the Pacific and Australian plates in a hotspot reference
frame with no net rotation [Gripp and Gordon, 2002]. The thin black arrow shows motion of the Pacific plate relative to the Australian plate
averaged over 20 Ma.
portion of the South Island beneath the Marlborough Fault Zone. Here four major strike-slip faults
accommodate much of the motion: the Wairau, the Awatere, the Clarence, and the Hope faults [e.g., Wallace
et al., 2007]. At the southern end of the Marlborough Fault Zone, slip transfers to the Alpine fault, which
accommodates 70–75% of plate motion between the Pacific and Australian plates [Norris and Cooper, 2001].
The Alpine fault extends southward into Fiordland where the Australian plate subducts beneath the Pacific
plate at the Puysegur Trench and beneath Fiordland.
Previous studies of SKS phases found that the mantle underlying the South Island of New Zealand is highly
anisotropic (Figure 1) [Klosko et al., 1999; Duclos et al., 2005]. Central portions of the South Island, as well as its
northern end, exhibit orientations of fast quasi-shear waves nearly parallel to the trend of the Southern Alps.
These regions also exhibit large delay times between fast and slow quasi-shear waves, ranging between 1
and 2 s. The southernmost regions of the island show orientations of the fast quasi-shear wave rotated
approximately 20° counterclockwise from those measurements in the northern portion of the island, though
delay times remain between 1 and 2 s. Shear wave splitting measurements made on both the Chatham
Islands and Macquarie Island (both lying roughly 1000 km from the South Island) exhibit different orientations
and amounts of anisotropy from what is observed on the South Island. All measurements made on the
Chatham Islands yield nulls, suggesting isotropy. Those from Macquarie Island show a NW fast axis orientation
with a delay time of over 1 s [Klosko et al., 1999]. These results suggest that the observed anisotropy in the
mantle under the South Island is not due either to older structures found throughout the South Island, as
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
1021
Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
A
B
LITHOSPHERIC DEFORMATION
ASTHENOSPHERIC DEFORMATION
Figure 2. Cartoons showing the proposed mechanisms of deformation, traversing the South Island perpendicular to the Alpine fault. Light
areas represent regions deforming via dislocation creep, thus producing a lattice-preferred orientation. (a) A model with a weak lower crust
and strong mantle lithosphere in which dislocation creep occurs as in a thin viscous sheet. (b) A model with a strong lithosphere such that
localized strain and lattice-preferred orientation develops in the asthenosphere in a region fanning out from the base of the lithosphere.
suggested by Furlong [2007], or to absolute plate motion of the Pacific or Australian plates [Klosko et al., 1999],
as is observed at the East Pacific Rise [Wolfe and Solomon, 1998]. Studies of shear wave splitting of S arrivals from
local earthquakes in the subduction zones yield much smaller delay times than those of SKS phases, but it has
been difficult to determine whether the smaller values are caused by low anisotropy in the mantle lithosphere
or by frequency-dependent splitting [Audoine et al., 2000; Karalliyadda and Savage, 2013].
Two explanations for the observed pattern of anisotropy have been proposed (Figure 2). In one, anisotropy is
caused by shear within the mantle lithosphere across a broad zone that spans the width of the South Island, if
not wider [Molnar et al., 1999; Little et al., 2002; Moore et al., 2002], an interpretation invoked in other strikeslip regions [e.g., Vauchez and Nicolas, 1991]. GPS studies also suggest that, at least for central portions of the
South Island, simple shear likely occurs over a zone approximately 200 km wide [e.g., Houlié and Stern, 2012].
Others have inferred that localized deformation in the shallow lithosphere around the Alpine fault continues
through the lithosphere into the asthenosphere so that the source of the anisotropy extends to depths of
250 km or more [Klosko et al., 1999; Karalliyadda and Savage, 2013]. Both interpretations rely on data recorded
only by stations deployed across the South Island of New Zealand. As the maximum width of the South Island
is approximately 200 km, this limits the lateral extent of the array aperture. Thus, to test these proposed
mechanisms of deformation, we devised an experiment that expanded the array aperture.
2. The Marine Observations of Anisotropy Near Aotearoa Experiment
The Marine Observations of Anisotropy Near Aotearoa (MOANA) experiment included a 1 year deployment of
ocean bottom seismometers (OBSs) installed off both coasts of the South Island of New Zealand from late
January 2009 to early February 2010 (Figure 1). Deployed with approximately 100 km spacing, this array of
OBSs increased the aperture of study to 5 times the width of the South Island. Stations NZ01–NZ04 rested on
oceanic crust, with the others lying on the continental shelf surrounding New Zealand. All instruments
recorded continuously at a sample rate of 50 Hz. These OBSs complemented the existing land stations of the
New Zealand National Seismograph Network maintained by GeoNet. All but one of the OBSs (station NZ14)
were equipped with Trillium 240 seismometers with the final OBS equipped with a Trillium 40 seismometer.
The former are broadband instruments with flat frequency responses between 240 s and 35 Hz. The latter is
an intermediate period instrument with a long-period corner at 40 s. Although 30 instruments were deployed,
one did not yield usable seismograms (station NZ01), and one was never recovered (station NZ17).
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
We used Rayleigh wave polarizations to orient the horizontal components of the OBSs [Stachnik et al., 2012].
This technique exploits the elliptical particle motion of Rayleigh waves and the fact that this motion is
theoretically observed only on the vertical and radial components of ground motion. Since linearity is easier
to assess than ellipticity, Stachnik et al. [2012] determined instrument orientation by cross correlating the
vertical component with the Hilbert transformed radial component. The polarization analysis included first
predicting the arrival time of the Rayleigh wave with a group speed of 4.0 km/s and then applying a bandpass filter from 0.02 to 0.04 Hz to the waveform in the window 20 s before and 600 s after this phase arrival.
The Hilbert transformed radial components for a range of back azimuths (0°–360°) were cross correlated
with the vertical components. The sensor orientation is assumed to correspond to the azimuth of maximum
correlation. For the OBSs associated with the MOANA experiment, between 10 and 31 events were used to
determine the orientations of the horizontal components.
3. Mantle Anisotropy and Shear Wave Splitting Methods
Within a single anisotropic layer, a traveling shear wave splits into two, orthogonal quasi-shear waves that
propagate through the medium with different wave speeds, resulting in two distinct arrivals on a seismogram [Babuška and Cara, 1991, and references therein]. Shear wave splitting analyses yield measurements of
both the delay time between the fast and slow quasi-shear waves (δt) and the orientation (φ) of the faster
quasi-shear wave. These parameters provide information on the orientation and degree of anisotropy within
the medium of interest.
In the upper mantle, anisotropy is dominantly a result of lattice-preferred orientation (LPO) or the preferential
alignment of crystalline structure in response to finite strain [e.g., Silver, 1996; Savage, 1999]. Anisotropy is
commonly quantified as a percentage: 100(vmax vmin)/vavg, where vmax is the speed of the fast quasi-shear
wave, vmin is that of the slow quasi-shear wave, and vavg is the average of the two. It is typically thought that
olivine is the principal mineral involved in upper mantle anisotropy, for which percent anisotropy can reach
18% for single crystals, though crystals not aligned in the same direction yield a smaller overall percent anisotropy. Other minerals such as orthopyroxene also contribute [e.g., Kumazawa, 1969; Ribe, 1992; Long and
Becker, 2010; Skemer et al., 2012]. Deformation in the upper mantle occurs via either diffusion creep or dislocation creep [e.g., Karato and Wu, 1993]. Diffusion creep involves the diffusion of atoms along grain
boundaries, whereas dislocation creep involves the migration of dislocations in the crystal lattice [Turcotte
and Schubert, 2002]. In general, only dislocation creep produces the LPO and microstructure consistent with
observed anisotropy in the upper mantle [e.g., Savage, 1999].
Laboratory experiments suggest that predicted lattice-preferred orientation patterns in olivine aggregates
depend on the finite strain [e.g., Karato et al., 2008]. At low strain and/or when dynamic recrystallization is
limited, the anisotropy of a deformed aggregate can be expressed relative to the principal axes of finite strain.
During progressive simple shear (e.g., the Alpine fault), the olivine a axes initially orient approximately 45°
from the plane of shear and rotate progressively toward that plane as strain accumulates; at sufficiently high
strains (>150% in lab samples deformed at 1300°C) and/or cases where dynamic recrystallization is prevalent,
the olivine a axes rotate to lie within the plane of shear [e.g., Zhang and Karato, 1995]. With moderate
hydrogen (“water”) content (~500 ppm H/Si), such as might be expected in the asthenosphere or within the
mantle wedge of a subduction zone, a different pattern of LPO (E-type) is observed [e.g., Mehl et al., 2003;
Karato et al., 2008]. Examination of fabrics in high-temperature shear zones (1000–1200°C) demonstrates that
the details of how LPO evolves with progressive simple shear in the Earth match those determined in the lab
and that the olivine water content under which the fabric transitions occur is consistent with measurements
of water contents preserved in the natural samples [e.g., Warren et al., 2008; Skemer et al., 2010, 2013]. The
agreement between the laboratory and natural observations justifies interpretations of mantle anisotropy
guided by the details of the laboratory analyses. Finally, B-type and C-type LPOs observed in lab samples
deformed at higher water contents, pressures, and stresses than those required to promote E-type fabric can
significantly influence the interpretation of anisotropy [e.g., Karato et al., 2008].
To constrain the fast axis orientations and delay times, we employ the method outlined by Silver and Chan
[1991] as implemented in SplitLab [Wüstefeld et al., 2008]. This is a grid search-based method that determines
the best fitting splitting parameters (φ and δt) by minimizing energy on the transverse component after removing effects due to shear wave splitting. We also adopt the multiple event splitting method of Wolfe and
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
Figure 3. Locations of earthquakes used in this study. All events shown yielded at least one usable measurement. Circles represent
events used to constrain splitting parameters only on land stations. Diamonds represent events recorded on both land and ocean
bottom seismometers.
Silver [1998] in which the resulting energy contours of individual measurements are stacked. This helps
reduce effects of acknowledged shortcomings of Silver and Chan’s method in which large amounts of
noise and/or small degrees of birefringence can yield incorrect values of φ and δt [Restivo and Helffrich,
1999; Levin et al., 2007; Monteiller and Chevrot, 2010]. In such instances, the measured value of φ lies
parallel to the back azimuth of the earthquake used in the analysis, with the result that Silver and Chan’s
method can yield unrealistically large values of δt. Such measurements are typically classified as null
measurements. Because the ocean is inherently a noisy environment, many splitting measurements
exhibited these characteristics, which makes it difficult to distinguish null measurements from cases with
low signal-to-noise ratios (defined as the ratio of the maximum amplitude on the radial component to
the standard deviation of the transverse component in the analysis window). With the stacking method
of Wolfe and Silver [1998], however, we were able to use such measurements to distinguish noisy
waveforms and/or small delay times from nodal results.
4. Results
We examine all SKS, SKKS, and PKS arrivals from earthquakes with magnitude Mw ≥ 5.0 recorded across the
MOANA array between early 2009 and early 2010, as well as by the New Zealand National Seismograph
Network between 2003 and April 2012, which included 28 stations on the South Island, Stewart Island, and
the Chatham Islands. Since the last major study of SKS phases in New Zealand [Duclos et al., 2005], several new
stations were added to the network, and we could also use more than 8 years of new waveform data from
those previously characterized stations. Although we analyzed earthquakes of magnitude Mw ≥ 5.0 occurring
at epicentral distances between 85° and 130° from the South Island, we found all useable events to be of
magnitude Mw > 6.0 with epicentral distances between 90° and 120°. All the useable phase arrivals were SKS,
with one useable SKKS arrival. The majority of the events occurred in the Aleutian, Kuril, and Peru-Chile
subduction zones, resulting in nonuniform back azimuthal coverage, especially on the OBSs (Figure 3 and
Table 1). This nonuniform back azimuthal coverage on the OBSs means that we cannot resolve any possible
two-layer anisotropy [Silver and Savage, 1994].
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
1024
Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
Table 1. List of Earthquakes Used in This Studya
ZIETLOW ET AL.
Year
Julian Day
Latitude (°)
Longitude (°)
Depth (km)
Mw
BAZ (°)
2003
2003
2003
2003
2003
2003
2003
2003
2003
2003
2004
2004
2004
2004
2004
2004
2004
2004
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2008
2008
2008
2008
2008
2008
2008
2008
2008
022
050
076
166
167
174
265
270
301
339
120
162
180
283
320
325
333
353
018
080
141
164
165
165
166
168
264
269
288
339
023
053
110
130
165
173
189
236
265
273
274
293
317
013
055
068
119
150
196
210
214
227
230
246
253
318
320
353
355
360
035
063
106
107
141
179
180
187
239
18.77
53.65
51.27
51.55
55.49
51.44
19.78
50.04
43.84
55.54
10.81
55.68
54.8
11.42
4.7
13.38
43.01
48.46
42.95
24.98
3.29
19.99
51.23
51.23
41.3
40.77
43.89
5.68
46.82
6.22
6.86
21.32
60.95
52.51
51.75
45.42
51.21
51.15
26.87
46.35
46.47
13.46
26.04
46.24
7.01
43.22
52.01
52.14
52.48
53.64
51.31
13.39
13.81
45.84
2.98
22.25
2.31
51.36
51.36
52.58
20.17
46.41
51.85
51.88
51.16
11.01
10.85
53.88
7.64
104.1
164.64
177.98
176.92
160
176.78
70.67
87.81
147.75
165.78
86
160
134.25
86.67
77.51
90.06
145.12
156.31
144.87
63.47
80.99
69.2
179.41
179.41
125.97
126.57
146.15
76.4
154.11
29.83
77.79
33.58
167.09
169.26
177.08
149.34
179.31
157.52
63.15
153.17
153.24
76.68
63.22
154.52
80.49
133.53
179.97
157.29
168.05
169.7
179.97
76.6
76.29
150.06
77.97
69.89
77.84
179.52
178.98
168.2
70.04
153.18
179.36
179.16
178.76
91.82
91.71
152.89
74.38
24
19
33
20
175
20
10
16
65
10
10
189
20
35
15
41
39
11
42
579
40
116
51
51
10
10
103
115
43
22
14
11
22
18
14
95
22
43
598
11
19
23
552
10
23
441
117
116
10
26
21
39
30
94
31
40
123
29
30
35
44
10
10
13
27
17
15
633
154
7.5
6.6
7.0
6.5
6.9
6.9
6.4
7.3
5.8
6.6
6.2
6.8
6.8
6.9
7.2
6.3
7.0
6.2
6.2
6.8
6.3
7.8
6.8
6.8
7.2
6.6
6.0
7.5
6.1
6.8
6.2
7.0
7.6
6.4
6.5
6.0
6.6
6.5
6.0
6.6
6.5
6.7
6.8
8.1
6.3
6.0
6.2
6.4
6.1
5.9
6.7
8.0
6.0
6.2
6.8
7.7
6.8
7.2
6.3
6.4
6.3
6.5
6.5
6.6
6.3
6.6
6.1
7.7
6.4
72.1
14.3
3.4
2.7
352.8
2.6
91.8
313.3
343.7
356.2
88.9
352.8
30.2
88.9
100.5
85.2
342.6
351.5
343.2
131.0
103.3
123.0
6.7
4.8
44.4
41.9
342.9
108.9
351.1
223.5
98.7
221.7
359.0
13.9
4.8
346.3
7.3
353.4
131.7
349.1
349.9
117.7
135.4
347.6
110.7
334.2
7.5
352.1
13.4
0.2
6.7
117.5
118.3
347.1
104.5
124.6
109.7
7.9
8.2
14.5
122.5
349.8
5.0
8.0
357.1
276.9
276.7
351.0
110.8
©2013. American Geophysical Union. All Rights Reserved.
1025
Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
Table 1. (continued)
Year
Julian Day
Latitude (°)
Longitude (°)
Depth (km)
Mw
BAZ (°)
2008
2008
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2010
2011
2011
2011
2011
2011
2011
2011
2011
2011
2012
2012
2012
2012
286
329
015
033
040
046
089
097
103
107
108
111
123
187
222
264
267
286
317
318
321
344
358
010
012
037
049
089
103
126
144
169
181
199
216
224
246
281
357
001
097
171
175
245
279
301
326
345
057
065
080
102
20.12
54.2
36.86
13.58
6.57
5.85
56.55
46.05
33.17
19.58
46.01
50.83
14.57
50.44
14.10
27.33
18.82
52.75
19.39
22.97
52.13
53.42
42.23
40.65
18.45
46.84
42.59
13.67
33.17
18.06
8.08
44.45
16.4
52.88
51.42
1.27
51.45
51.37
53.13
26.79
17.21
21.7
52.07
52.17
24.18
14.44
15.36
17.84
51.71
28.25
16.5
18.23
64.97
154.32
155.15
76.56
81.15
80.89
152.74
151.55
96.55
70.48
151.43
155.01
91.17
176.99
92.89
91.44
107.35
167.00
70.32
66.64
131.40
152.76
134.70
124.69
72.55
152.73
130.7
92.83
96.55
70.55
71.56
148.69
97.78
169.71
178.65
77.31
175.87
175.36
171.16
63.09
94.34
68.23
171.84
171.71
64.22
75.97
65.09
99.96
95.99
63.29
98.22
102.69
353
492
36
21
15
21
21
31
17
25
35
152
124
22
5
14
10
24
27
220
3
656
411
29
13
30
578
34
17
37
581
25
20
25
27
207
24
19
18
577
166
128
52
32
15
24
550
54
12
554
20
20
6.2
7.3
7.4
6.0
5.9
6.0
6.0
6.9
6.9
6.1
6.6
6.2
6.3
6.1
7.5
6.1
6.4
6.4
6.5
6.2
6.6
6.3
6.3
6.5
7.0
6.0
6.9
6.6
6.9
6.2
6.4
6.2
6.3
6.7
6.4
7.1
6.5
6.4
6.4
7.0
6.7
6.5
7.3
6.9
5.9
7.0
6.6
6.5
6.7
6.1
7.5
6.7
129.9
351.9
351.3
113.8
109.9
107.4
18.0
348.7
305.1
120.2
349.9
351.8
83.4
2.8
289.3
295.8
72.6
15.9
127.1
132.0
35.3
352.1
331.4
47.0
93.3
348.1
323.7
279.6
304.7
123.1
118.4
336.0
80.3
13.5
8.4
109.4
0.5
10.4
1.9
135.9
81.2
129.2
9.5
12.4
132.0
118.9
128.1
74.3
318.8
132.5
81.2
76.8
a
Bold events are recorded on an OBS.
The waveforms were band pass filtered between 0.03 Hz and 0.08 Hz with a four-pole Butterworth filter.
Microseismic noise determined the high-frequency end of this filter. Since the OBSs rested atop sediment, the
instruments were subject to long-period noise, which determined the low-frequency end of the filter.
Furthermore, we ignore waveforms with signal-to-noise ratios less than 5, consistent with what Wüstefeld and
Bokelmann [2007] found as the lowest limit for automatic detection of null measurements. The analysis
window included 20–40 s of preevent noise, with the end of the window typically limited by predicted arrivals of later seismic phases.
Individual measurements before stacking varied in quality from station to station (Figure 4). Typically on the
OBSs, SKS arrivals were clear on the filtered waveforms, but relatively high noise levels affected some
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Figure 4. Examples of splitting measurements showing (first column) the filtered waveforms with analysis windows depicted by grey shading, (second column) the waveforms corrected
first for delay time and then for (third column) both delay time and orientation of the fast quasi-shear wave, the particle motion before (dashed blue line) and after (solid red line) the (fourth
column) effects due to splitting are removed, and (fifth column) resulting contours of transverse energy. The filled grey contour represents the 95% confidence region of δt-φ space. The
dashed blue lines in the seismogram in the left column are the radial components and the solid red the transverse. (a) Event 2010010 recorded at NZ08. (b) Event 2009097 recorded at NZ12.
(c) Event 2009108 recorded at NZ15. (d) Event 2009222 recorded at NZ30. (e) Event 2004320 recorded on WVZ. Event details are in Table 1.
ZIETLOW ET AL.
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measurements (Figures 4b and 4c). This is evident by the absence of linearized particle motions as well as
the large 95% confidence intervals calculated for splitting measurements at such stations. Some
measurements on OBSs, however, were comparably precise to those made on land stations. These
waveforms (compare Figures 4d and 4e) have high signal-to-noise ratios, linear particle motions, and
tightly constrained splitting parameters.
Some stations yielded null measurements (Figure 4a). In such cases, an error ellipse contour elongated in the
δt direction for φ aligned parallel or perpendicular to the back azimuth and low energy on the raw transverse
component suggests either that there may be no anisotropy underlying the station or alternatively that the
azimuth of the fast orientation is parallel or perpendicular to the back azimuth of the event but with δt poorly
constrained. This is evident in the individual energy contours from station NZ09 seen in the left column of
Figure 5. Individual contours in Figure 5a–5d exhibit one of the shortcomings of Silver and Chan’s method,
discussed in the previous section. For each SKS phase, noise and/or small birefringence at this station forces
the predicted orientation of the fast quasi-shear wave along the back azimuth of the earthquake, with the
predicted delay time approaching the maximum allowed time in the analysis (in this case, 4.0 s). When the
contoured energy distributions are stacked, however, the resulting sum shows that these measurements are
consistent with one another and yield precise estimates of φ and δt (Figure 5e). Likewise, the individual
contours for earthquakes with different back azimuths in Figures 5f–5h from station NZ13 show clear
anisotropy; none reveals a tightly constrained orientation or delay time, but the resulting stack (Figure 5j)
does constrain φ and δt.
We also analyzed the individual seismograms for some measurements both before and after correcting for
anisotropy with the average φ and δt calculated from the stacked measurements at that station (Figure 6). The
averages for φ and δt obtained from the stack (Figure 7 and Table 2) are consistent with what the individual
measurements allow, suggesting that a one-layer model is sufficient to explain the data.
Stations NZ08, NZ22, and NZ23 yielded null measurements, though these are constrained by a single event
with a back azimuth parallel to the predicted orientation of the fast quasi-shear wave. Some stations, including stations NZ06, NZ07, NZ14, NZ19, and NZ21, yielded no useable measurements due to high levels of
noise in the waveforms. We should note that in analysis of DCZ, the north and east components of the
instrument were switched, consistent with phase arrivals in the seismic record.
In central portions of the South Island and within close proximity to the Southern Alps (a zone roughly
100–200 km wide), the orientations of fast polarization directions are nearly parallel to relative plate
motion (roughly 240°, as averaged over the past 20 Myr in a reference frame fixed to the Australian plate
[Cande and Stock, 2004]). Delay times are between about 1.5–2.0 s (Figure 7). In the extreme north of the
island, including the Marlborough Fault Zone, orientations of the fast quasi-shear wave remain nearly
parallel to relative plate motion with delay times again upward of 2.0 s; however, the mantle under some
of these stations may have interacted with, or even include, the subducting Pacific plate. In the southern
portion of the island, especially at stations > 100 km southeast of the Alpine fault, fast orientations are
more oblique to relative plate motion. In south central portions of the South Island, including DCZ, EAZ,
MLZ, PYZ, and WHZ (Figure 7), fast orientations are rotated approximately 40° counterclockwise from
plate motion. This obliquity increases to nearly 60–70° at stations near the southeastern coast of the
South Island (ODZ, OPZ, SYZ, and TUZ). Delay times observed at these stations remain around 1.0 s. On
both Stewart Island and the Chatham Islands, very little splitting is observed; delay times are only 0.4 s.
The fast orientation seen on Stewart Island is consistent with the obliquity seen elsewhere on the
southern portions of the South Island. Individual measurements made on the Chatham Islands yielded
null or near-null results, consistent with previous observations [Klosko et al., 1999]. Stacking these results
gives an observed fast orientation nearly E-W, but the calculated delay time is negligibly small (0.4 s),
and the number of events originating in the Aleutians and Kuril Trench may bias this result.
Within about 100 km offshore of the west coast, most shear wave splitting measurements yielded fast axis
orientations parallel (stations NZ11 and NZ15) or approximately parallel (station NZ12) to the orientation of
relative plate motion. As seen on land for those stations within 100 km of the Alpine fault, delay times observed at the OBSs range from just over 1 s up to 2.4 ± 0.7 s. At stations deployed around 200 km offshore the
west coast (i.e., stations NZ13, NZ16, and NZ18), delay times remain relatively large in magnitude around 1.5 s.
Unlike those OBSs immediately off the coast, these stations yielded fast orientations rotated between 40° and
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Figure 5. (a–d) Individual energy contours from individual splitting measurements made at NZ09. (e) Resulting stack of contours shown in
Figures 5a–5d. (f–i) Individual energy contours from NZ13. (j) Stack of individual energy contours from NZ13 shown in Figures 5f–5i. The grey
contour is the 95% confidence interval. The intersection of the black lines defines the best fitting splitting parameters.
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Figure 6. (top) Superposition of the fast (φ direction) and slow (φ + 90°) components and (bottom) the uncorrected and corrected particle motions for (left) event 2009321 and (right) event
2009344 at NZ09.
50° counterclockwise from relative plate motion. Beyond 300 km from the west coast, we observed a region
with little to no resolvable anisotropy. The stations with minor resolvable anisotropy in this region (stations
NZ05 and NZ09) show fast axes rotated almost 90° to that of relative plate motion with delay times around
0.5 s. The only useable measurement at station NZ08 yielded a null result.
Figure 7. Summary of SKS splitting measurements made in this study. Red bars indicate orientations of the polarizations of the faster quasi-shear wave, and black crosses indicate null
measurements. Grey wedges define uncertainties in measured orientations of fast quasi-shear waves (uncertainties are also found in Table 2). Black dots mark stations at which no useable measurements were made. Thick black arrows show current absolute plate motion of the Pacific and Australian plates in a hotspot reference frame with no net rotation [Gripp and
Gordon, 2002]. The thin black arrow shows plate motion relative to the Australian plate averaged over 20 Ma. SKS splitting measurements from Klosko et al. [1999] and Duclos et al. [2005]
plotted in light grey.
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Table 2. Summary of Splitting Results by Station, Utilizing the Wolfe and Silver [1998] Stacking Method
Station
δt (s)
Error δt (s)
φ (°)
Error φ (°)
No. of Events
NZ02
NZ03
NZ04
NZ05
NZ06
NZ07
NZ08
NZ09
NZ10a
NZ11a
NZ12a
NZ13a
NZ14
NZ15a
NZ16a
NZ18
NZ19
NZ20
NZ21
NZ22
NZ23
NZ24
NZ25
NZ26
NZ27
NZ28
NZ29
NZ30
APZ
CRLZa
CTZ
DCZ
DSZa
EAZa
FOZa
JCZa
KHZ
LBZa
LTZ
MLZ
MQZa
MSZ
NNZ
ODZa
OPZ
OXZa
PYZ
QRZ
RPZa
SYZ
THZ
TUZ
WHZ
WKZa
WVZa
0.8
0.6
0.7
0.5
null
0.7
0.7
1.2
1.8
1.5
2.4
1.5
1.6
0.8
null
null
0.5
0.8
0.6
0.4
1.2
1.3
1.0
0.4
1.0
0.4
1.8
2.0
1.0
1.6
0.8
1.2
1.0
1.6
1.0
0.8
1.4
1.4
1.0
0.4
1.2
1.2
2.0
1.6
0.8
1.4
1.2
1.4
1.2
2.0
0.5
0.2
0.2
0.5
null
0.2
0.3
1.3
0.8
0.4
0.7
0.7
0.6
0.2
null
null
0.3
0.1
0.3
0.2
0.4
0.2
0.1
0.1
0.2
0.1
0.2
0.4
0.2
0.2
0.1
0.1
0.1
0.2
0.1
0.1
0.2
0.2
0.2
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
17.2
13.1
11.1
3.0
39.0/129.0
15.2
11.1
69.8
21.2
11.1
49.6
13.1
23.3
51.6
78.0/12.0
68.0/22.0
51.6
45.5
49.6
47.5
47.5
9.1
27.3
7.1
13.1
88.0
1.0
51.6
19.2
43.5
33.4
25.3
41.5
31.4
19.2
3.0
27.3
39.4
15.2
27.3
41.5
13.1
43.5
39.4
29.3
47.5
1.0
17.2
47.5
49.6
24.3
10.1
10.1
40.5
4.0
16.2
18.2
40.5
4.0
4.0
12.1
4.0
6.1
10.1
4.0
12.0
24.3
8.1
20.2
18.2
12.1
4.0
12.1
8.1
4.0
4.0
4.0
10.1
4.0
2.0
2.0
4.0
4.0
4.0
2.0
4.0
6.1
4.0
4.0
12.1
4.0
6.1
2.0
4.0
12.1
2.0
2.0
2.0
6.1
2.0
4
8
6
3
1
4
5
3
2
4
2
4
3
4
1
1
4
8
5
4
3
5
5
35
21
23
21
6
29
25
22
28
35
21
24
10
11
23
32
13
14
13
21
30
13
23
23
19
27
25
a
Stations that lie in the central portion of the South Island within 200 km of the center of the shear zone. We used only these stations in
the error calculations found in Table 3 and in Figures 8–10.
The three stations deployed off the continental shelf and on oceanic lithosphere (NZ02–NZ04)
also exhibit a very different sense of anisotropy, with fast axis orientations trending almost due
north and delay times around 0.7 s. Offshore of the east coast, fast directions are consistently
nearly perpendicular to relative plate motion between the Pacific and Australian plates. Delay
times calculated at these stations also remained consistent across the region, ranging between
about 0.5 and 1.0 s.
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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5. Relationship of Anisotropy to Mantle Deformation
The shear wave splitting results clearly indicate a finite width over which the observed anisotropy could be
due to simple shear between two plates. Off the east coast, the orientations of the fast quasi-shear waves are
nearly aligned with current absolute plate motion of the Pacific plate calculated from HS3-NUVEL1A with no
net rotation (Figure 7) [Gripp and Gordon, 2002]. Likewise, the fast orientations measured at the OBSs
deployed off the west coast on oceanic lithosphere appear oriented parallel to absolute plate motion of the
Australian plate. Offshore the west coast at stations deployed on the continental shelf, there is a decrease in
the magnitude of the delay times as well as increase in the counterclockwise rotation of the fast axis orientations with increasing distance from the South Island. Furthermore, at distances 300 km and greater from
the west coast, there appears to be little observable splitting. Thus, areas of anisotropy generated by different
tectonic processes appear to bookend the region apparently affected by simple shear associated with relative plate motion. The symmetry of the anisotropy on either side of the Alpine fault in central regions of the
South Island is also interesting, since this implies that strain is relatively uniform on either side.
The general trend of decreasing delay time observed off the west coast from the northeast toward the
southwest (i.e., NZ11, NZ12, NZ14, and NZ15) is mimicked on land, with delay times of 2.0 s observed in the
extreme northwest of the island (QRZ) versus delay times of closer to 1.0 s observed in the southwest (i.e.,
JCZ). This feature may result from the more than 800 km of motion known to have occurred between the
Pacific and Australian plates over the past 45 Ma, with northwestern regions seeing more relative displacement compared to those farther south.
To discriminate between the two currently proposed mechanisms of deformation shown in Figure 2, we
compare these shear wave splitting results to predictions made from both a thin viscous sheet model
(mimicking distributed lithospheric deformation shown in Figure 2a) and a model in which strain within the
lithosphere is localized and anisotropy is produced by distributed strain in the asthenosphere (Figure 2b).
5.1. Lithospheric Deformation: Thin Viscous Sheet Model
For a thin viscous sheet, we follow England et al. [1985]. In such a model, horizontal components of velocity
are assumed to be independent of depth, a reasonable assumption when the tractions on the base of the
sheet are small compared to stresses within the sheet. They assume that deformation of the sheet obeys a
constitutive law of the following form: ε˙ ~ τ n, where ε̇ is strain rate, τ is deviatoric stress, and n is the exponent
of the non-Newtonian rheological model. From England et al. [1985], the approximate velocity field as a
function of distance from the deforming boundary decays as
4pffinπy
uðx; yÞ ≡ U0 sin 2 πx λ eð =λ Þ
(1)
where U0 is the component of velocity parallel to the deforming boundary (18 mm/yr in this study or half the
total observed relative plate motion [Beavan et al., 1999]), x is the parallel distance along the boundary, λ is
the wavelength of deformation (twice the length of a deforming boundary of finite length), and y is the perpendicular distance from the boundary. In this study, we assume that n = 3. Equation (1) is most accurate near
the maxima and minima of the horizontal velocity (i.e., when x is close to λ/4) [England et al., 1985].
With exponentially decreasing velocity and strain, approximately 75% of relative plate motion occurs where
y < 2y0, where y0 is the e-folding width (the value of y where the velocity decays to 1/e of its original value) of
equation (1):
pffiffiffi
(2)
y 0 ¼ λ ð4 nπÞ
We note that England et al. [1985] formulated equation (1) for a semiinfinite region in the x-y plane for y > 0
and therefore for only one side of a deforming boundary. As we are concerned with predicted motion on
both sides of a deforming boundary, we assume symmetry in the velocity field. Thus, we define the total
width of deformation due to the deforming boundary as 4y0, again within which approximately 75% of the
relative displacement of the plates has been accommodated. For a fixed exponent of the non-Newtonian
rheological model n, equation (2) indicates that for a given value of y0, there is a corresponding value of λ, the
along-strike wavelength of deformation. Since λ is twice the length of the deforming boundary, we can also
predict the length of the deforming boundary from y0 or from an inferred width of deformation.
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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5.2. Asthenospheric Deformation
For the case of shear in the asthenosphere, strain rate decreases with depth in a fan-like shape beneath the
lithosphere-asthenosphere boundary (Figure 2b). Where the strain rate becomes sufficiently small, dislocation creep is no longer the dominant mechanism of deformation, and lattice-preferred orientation does not
develop. Assuming that strain from absolute plate motion is negligible compared to the strain generated in
the fan-like shape beneath the fault, and assuming a constant viscosity in the asthenosphere, we adopt a
toroidal velocity field of the following form, in which the only nonzero component is that parallel to what is
assumed to be a fixed boundary [Savage et al., 2004]:
. uy ≡ U0 1 2θ
;
(3)
π
where U0 again is the component of velocity parallel to a strike-slip boundary (U0 = 18 mm/yr), θ = arcsin(z/r),
r = (y2 + z2)^(1/2), z = depth, and y = perpendicular distance from the fault. The only nonzero component of
the strain rate tensor for this velocity field is [Savage et al., 2004]
ε̇ ¼ ±U0 πr :
(4)
To determine whether or not a transition from dislocation to diffusion creep is feasible at a specified depth
given the strain rates predicted from equation (4), we use the synthesis of laboratory experiments given by
Hirth and Kohlstedt [2003]. The strain rate of minerals in a steady state is
ε̇ ¼ Aσ m d p C OH r exp½ðE þ PV Þ=ðRT Þ;
(5)
where ε̇ is the strain rate, A is a preexponential factor, σ is shear stress, m is the stress exponent, p is the grain
size exponent, d is grain size, COH is water content, r is the water content exponent, E* is the activation energy,
P is pressure, V* is the activation volume, R is the gas constant, and T is temperature in Kelvin. In a dislocation
creep regime at constant OH concentrations (1000 H/106Si), A = 90 (for stress in megapascal, COH in H/106Si,
and grain size in micrometer), m = 3.5 ± 0.3, p = 0, r = 1.2, E* = 480 ± 40 kJ/mol, and V* = 11 × 10 6 m3/mol. In
a diffusion creep regime at constant OH concentrations (again, 1000 H/106Si), A = 1.0 × 106 (again, for stress in
megapascal, COH in H/106Si, and grain size in micrometer), m = 1, p = 3, r = 1, E* = 335 ± 75 kJ/mol, and
V* = 4.0 × 106 m3/mol. We calculate pressure by assuming it is 1 GPa at the base of the crust with a pressure
gradient of 30 MPa/km below this. At the lithosphere-asthenosphere boundary, we assume a temperature of
1573 K, with an adiabatic gradient of 0.5 K/km deeper into the asthenosphere. The unknowns for which we
must solve in equation (5) are shear stress and grain size.
To solve for these unknown parameters, we first predict strain rate as a function of depth using equation (4).
Given this strain rate, the temperature and pressure at a specified depth, and the parameters for dislocation
creep listed above, we next predict the shear stress required to yield the same strain rate given by equation (4)
using the flow law given in equation (5) for dislocation creep (i.e., when p = 0). Then, using this predicted shear
stress, we determine the corresponding grain size that gives the same strain rate using equation (5) in
its diffusion creep form (i.e., when p = 3). For instance, if the transition between dislocation creep and
diffusion creep occurred 100 km into the asthenosphere (z0 = 100 km, where z0 is the distance from the
lithosphere-asthenosphere boundary to the depth of the transition between dislocation and diffusion
creep directly under the deforming boundary), this model would require a shear stress of ~0.2 MPa and
a grain size of ~6 mm. For a transition at 150 km into the asthenosphere (z0 = 150 km), a shear stress of
~0.2 MPa and a grain size of ~7 mm is required, and a transition at 200 km below the lithosphere-asthenosphere
boundary also requires a shear stress of ~0.2 MPa, but a grain size of ~8 mm. Although strain rate decreases with depth, stresses increase to compensate for the influence of activation volume in the factor
that includes it in equation (5).
5.3. Predicted Patterns of Anisotropy
To generate a predicted pattern of anisotropy from the models discussed above, we follow relationships
outlined in Ribe [1992] and Kaminski and Ribe [2002]. We first convert the predicted strain rates from each
model into strain following McKenzie and Jackson [1983], who showed that in the case of simple shear, strain
can be calculated by simply multiplying strain rate by the time over which the strain has accumulated.
Modeling by Savage et al. [2007] suggests that the widespread anisotropy observed on the South Island is
primarily a result of strike-slip deformation, with little effect from convergence. Thus, we ignore the
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Figure 8. Calculated RMS misfit in predicted orientation of the fast quasi-shear wave relative to motion between the Australian and Pacific
Plates and predicted delay time for (a) a model of lithospheric deformation and (b) a model for asthenospheric deformation.
compressional component of motion between the Pacific and Australian plates and assume all the strain
accumulation is due to finite simple shear parallel to relative motion between the Pacific and Australian
plates. Following Sutherland [1999], about 850 km of strike-slip motion has occurred between the Pacific and
Australian plates. We assume the time over which this strain accumulated is equal to the time required to
displace 850 km of the fault at the present rate of 36 mm/yr, yielding about 24 Ma and maximum strain rates
on the order of 1014 to 1015 s1. Although the predicted strain in the asthenosphere includes a plunge, we
examine only the horizontal projection of that strain.
Numerical models of polycrystalline flow [Kaminski and Ribe, 2002] suggest that at temperatures appropriate
for the asthenosphere, lattice-preferred orientation develops in three stages. For strains less than 0.2, the LPO
follows the evolution of the finite strain ellipsoid. For strains between 0.2 and 1.2, however, the LPO evolves
faster than the finite strain ellipsoid, which Kaminski and Ribe [2002] parameterize using a model for dynamic
recrystallization. We estimate orientations for such strains from the mean orientation of the olivine a axis in
simple shear given in Kaminski and Ribe [2002]. For strains larger than 1.2, olivine a axes reach a steady state
orientation within the shear plane parallel to the shear direction. We note that Zhang and Karato’s [1995]
experiments, used by Kaminski and Ribe [2002], were conducted at high temperatures (1300°C), and although
others have shown similar relationships at slightly lower temperatures of 1200°C [Bystricky et al., 2000], tests
of Kaminski and Ribe’s [2002] parameterization have not been made for lithospheric temperatures.
Using laboratory-based flow laws for single crystals, Ribe [1992] calculated percent anisotropy as a function of
natural strain for olivine aggregates. We used Ribe’s [1992] relationship for an aggregate composed of 70%
ZIETLOW ET AL.
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Table 3. Calculated RMS Misfits Between Shear Wave Spitting Measurements Made in This Study and Predictions From Both a Thin
Viscous Sheet Model Representing Lithospheric Deformation (LD) and a Model Representing Asthenospheric Deformation (AD)a
Lithospheric Deformation
LD (4y0 = 40 km)
LD (4y0 = 60 km)
LD (4y0 = 80 km)
LD (4y0 = 100 km)
LD (4y0 = 120 km)
LD (4y0 = 140 km)
LD (4y0 = 160 km)
LD (4y0 = 180 km)
LD (4y0 = 200 km)
LD (4y0 = 220 km)
LD (4y0 = 240 km)
LD (4y0 = 260 km)
LD (4y0 = 280 km)
LD (4y0 = 300 km)
RMS Misfit φ (°)
RMS Misfit δt (s)
Asthenospheric Deformation
RMS Misfit φ (°)
RMS Misfit δt (s)
19.1
18.7
18.7
18.3
18.6
19.2
20.1
21.3
23.1
24.7
26.2
27.2
28.0
28.7
1.0
1.0
0.9
0.8
0.7
0.7
0.7
0.9
0.9
0.9
0.9
0.9
0.9
0.9
AD (z0 = 50 km)
AD (z0 = 60 km)
AD (z0 = 70 km)
AD (z0 = 80 km)
AD (z0 = 90 km)
AD (z0 = 100 km)
AD (z0 = 110 km)
AD (z0 = 120 km)
AD (z0 = 130 km)
AD (z0 = 140 km)
AD (z0 = 150 km)
AD (z0 = 160 km)
AD (z0 = 170 km)
AD (z0 = 180 km)
19.1
19.1
20.6
19.6
19.1
18.4
18.2
18.3
18.2
19.9
20.7
20.7
20.7
21.7
0.9
0.9
0.9
0.9
0.9
0.9
0.9
1.0
1.0
1.1
1.1
1.1
1.2
1.2
a
Only those measurements in the central portion of the South Island and within 200 km of the Alpine fault were included in the error
calculation (see Table 2).
olivine [Ribe, 1992, equation (24)] to convert our calculations of strain from each model to percent anisotropy.
To predict approximate delay times from percent anisotropy, we simply multiply percent anisotropy by the
layer thickness over shear wave speed, assuming that for predicted strain larger than 1.2, percent anisotropy
is 10%, which is reasonable given estimates of percent anisotropy from Pn studies [Bourguignon et al., 2007;
Scherwatch et al., 2002]; however, since the delay time between fast and slow quasi-shear waves depends on
both the magnitude of anisotropy and the thickness of the anisotropic layer, we do not emphasize the absolute magnitude of the predicted delay times. Instead, we use them to address relative variations in delay
time as a function of distance from the deforming boundary. In the case of a thin viscous sheet, we assume a
lithospheric thickness of approximately 100 km, based on estimates of lithospheric thickness used in other
studies [e.g., Stern et al., 2000]. By making such an assumption, we also ignore any crustal contribution to
anisotropy, of which average delay times range from approximately 0.2 to 0.3 s for the South Island
[Karalliyadda and Savage, 2013]. There is some agreement between the fast directions of local S phases made
in Karalliyadda and Savage [2013] and the teleseismic SKS measurements made in our study, especially for
southern portions of the South Island. Yet the smaller delay times calculated by Karalliyadda and Savage
[2013] than those measured using SKS phases suggest that the bulk of the anisotropy must at least be deeper
than the crust. For anisotropy in the asthenosphere, we assume an isotropic lithospheric thickness of 100 km,
and we estimate a thickness of the underlying anisotropic zone as a function of the value chosen for z0 as
discussed in the previous section. We assume a shear wave speed of 4.5 km/s.
6. Discussion
Our shear wave splitting measurements (Figure 7) indicate that large anisotropy with the orientation of the
fast quasi-shear wave nearly parallel to the direction of relative plate motion spans a zone approximately
100–200 km wide in central portions of the South Island. We estimate relevant parameters for our two
models, namely, the width of deformation (4y0) and corresponding length of the deforming boundary (λ/2)
for the thin viscous sheet model, and shear stress (σ) and grain size (d) for a model of asthenospheric shear.
Calculated RMS misfits for the orientation of the fast quasi-shear wave and delay time between our shear
wave splitting measurements and these predictions for the central portion of the South Island (Figures 8a and
8b and Table 3) show that both the lithospheric deformation and asthenospheric shear models can be made
to fit the data comparably well. This is not surprising since we chose model parameters so that the predicted
patterns match the observed patterns.
A thin viscous sheet model with a deformation width between 4y0 = 100 and 140 km (Figures 9b, 9c, and 10)
yields a predicted pattern of anisotropy similar to that observed (Figure 9a). These widths of deformation
correspond to a deforming boundary length (λ/2) around 544–762 km, consistent with the approximate
length of the boundary, as well as with ~850 km of displacement thought to have occurred between the
Pacific and Australian plates over the past 45 Ma [Sutherland, 1999; Cande and Stock, 2004]. Likewise, a model
of shear in the asthenosphere (Figures 9d, 9e, and 10) with a shear stress in the asthenosphere of
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
Figure 9. Comparison of observed shear wave splitting to predictions of the orientation of the fast quasi-shear wave relative to motion between the Pacific and Australian plates. Lengths correspond to delay time (δt). (a) Measurements made in this study. (b and c) Predictions
from a model for lithospheric deformation with a deforming zone width of 4y0 = 100–140 km, respectively. (d and e) Predictions from a
model for asthenospheric deformation with σ = 0.21 MPa and d ≈ 6 mm (corresponding to z0 = 100 km) and with σ = 0.22 MPa and d ≈ 7 mm
(corresponding to z0 = 130 km), respectively.
approximately 0.21–0.22 MPa and with an average grain size on the order of 6 ± 1 to 7 ± 1 mm (corresponding
to z0 = 100–130 km) also yields a similar pattern of anisotropy to that observed.
Given the long-period filter used in making the shear wave splitting measurements, individual SKS waves
sample a wider diameter along the geometrical raypath (i.e., larger Fresnel zone) than shorter period seismic
waves. Thus, the width of the deforming zone may be narrower than the 100–200 km zone we infer. Rümpker
and Ryberg [2000] show SKS phases with a dominant period of 16 s (similar to those we analyzed) arriving at a
station directly above an anisotropic region sample a region 140 km wide at the surface. This sampled region
becomes 180 km wide at 100 km depth and approximately 240 km wide at 200 km depth. Given the 100 km
spacing of the seismic stations and the clear difference in measured anisotropy between onshore the South
Island and offshore the east coast, there is no reason to think the width of the deforming zone is significantly
narrower than 100–200 km wide.
Thus, the question remains; given these model parameters and other currently available data on the
mantle characteristics of the South Island of New Zealand, are predictions from either model plausible? Specifically, is the lithosphere underlying the South Island and offshore thick enough to yield
large delay times similar to those observed from the teleseismic shear wave splitting measurements?
Are the shear stresses and grain sizes calculated here viable for producing anisotropy at
asthenospheric depths?
A shear wave speed of 4.5 km/s and 10% anisotropy requires a 90 km thick anisotropic layer to yield a delay
time of 2 s, similar to the largest delay times measured in this study. The crust offshore and in coastal areas of
the South Island is approximately 25 km thick [Salmon et al., 2013]. Under the Southern Alps, the thickness
increases to just over 40 km. Furthermore, recent work suggests that at temperatures below 700 ± 100°C,
olivine will not flow significantly at geologic stresses [e.g., Mei et al., 2010] and therefore will not produce a
lattice-preferred orientation. The modeling work of Savage et al. [2007] places the 700°C isotherm in the
40 km depth range for this region. Therefore, this would require a total lithospheric thickness of 130 km
(a 40 km thick isotropic region overlying a 90 km thick anisotropic region) for the anisotropy to be completely
accommodated within the lithosphere.
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Figure 10. (a) Orientations of polarizations of fast quasi-shear waves (relative to plate motion between the Pacific and Australian plates)
versus distance from the center of the shear zone. Negative and positive distances are for stations west and east of the center of the
shear zone, respectively. (b) Delay time versus distance from the center of the shear zone. In both Figures 10a and 10b, red circles indicate
those stations with fast direction orientations within 20° of the orientation of relative motion between the Pacific and Australian plates.
These represent those measurements from the central portion of the South Island reflecting simple shear along a deforming zone.
Determining the thickness of lithosphere remains a controversial topic, though evidence from P wave delays
suggest that the lithosphere beneath the axis of the South Island may have been thickened, perhaps by 2
times, from an original thickness of 100–120 km [Stern et al., 2000]. While this would imply a somewhat
deeper lithosphere-asthenosphere boundary than that inferred by other studies of surrounding regions [e.g.,
Rychert and Shearer, 2009; Fichtner et al., 2010], P wave tomography using local and regional events yielded a
high-velocity region to 180 km depth [Kohler and Eberhart-Phillips, 2002], suggesting lithosphere to this
depth. Thus, we deduce that the lithosphere could host the observed anisotropy over most of the study
region, especially given that larger delay times under portions of the Southern Alps might reflect
thickened lithosphere.
Our model of localized lithospheric deformation with shear in the asthenosphere predicts shear stresses and
grain sizes that fall within currently accepted ranges for such values. From the model strain rates and shear
stresses, we calculate an effective viscosity of the asthenosphere on the order of 1020 Pa s, consistent with
other studies [e.g., Conrad and Behn, 2010]. Furthermore, estimates of grain size in the asthenospheric upper
mantle range from several millimeters to centimeters [Hirth and Kohlstedt, 2003; Podolefsky et al., 2004; Becker
et al., 2008], making a grain size close to 6–7 mm (as required in this study) realistic.
More problematic is determining the grain size required for a transition from dislocation creep to diffusion
creep, and therefore, the transition from a region susceptible to the formation of lattice-preferred orientation
(dislocation creep) to one that is not (diffusion creep, see section 3). Some estimate this transition at about
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
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Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
200 km depth with a grain size around 1 cm [Hirth and Kohlstedt, 2003]. Later work investigated the effects of
hydration on the depth of this transition as well as grain size in oceanic mantle [Behn et al., 2009]. Behn et al.
[2009] found that for mantle lithosphere older than 60 Myr with an olivine water content of 1000 H/106Si,
grain size reached a minimum of 15–20 mm at ~150 km depth or 20–30 mm at ~400 km depth, values greater
than that predicted for the transition between dislocation creep and diffusion creep. Taking into account the
errors associated with the parameters used in equation (5), we calculate that the transition between the creep
mechanisms occurs for ranges of shear stress from 0.06 to 0.61 MPa and grain size from about 5 to 7 mm at
z0 = 100 km. For z0 = 130 km, shear stress ranges from 0.05 to 0.67 MPa, with grain size ranging from about 5
to 8 mm. These ranges for grain size are less than the steady state grain sizes proposed by Behn et al. [2009];
we do not have independent constrains on how large grain size could actually be in this region.
Concerning the role of water content on the evolution of LPO, laboratory experiments show that the influence of water on predicted anisotropy is largest when B-type or C-type fabrics are produced [e.g., Karato et al.,
2008, and references therein]. In these cases, the fast quasi-shear wave can be polarized normal, not parallel,
to the orientation of shearing (horizontal flow with B-type fabric; vertical flow with C-type). In the South Island
of New Zealand (at least in regions like the Southern Alps that lie outside of subduction zones), the water
content is likely not high enough to induce these fabrics. Furthermore, the shear stresses in the asthenosphere calculated from our localized lithospheric deformation model are low relative to those required to
promote B-type and C-type fabric. Thus, we infer that hydration of the asthenosphere does not strongly affect
anisotropy beneath New Zealand.
Although this SKS splitting study alone cannot definitively discriminate between distributed versus localized
modes of lithospheric deformation in the South Island of New Zealand, further analyses that can place a
depth extent on the anisotropy will aid in this debate. A study of Pn travel times also utilizing the data collected during the MOANA experiment (J. A. Collins and P. H. Molnar, manuscript in preparation, 2014) shows
fast Pn propagation for paths crossing the southeast side of the South Island to be aligned NNW-SSE, similar
to that of fast quasi-shear waves. Thus, the Pn data suggest that some of the shear wave splitting observed at
OBSs southeast of the island is within the lithosphere. Fast propagation of Pn for paths beneath most of the
island and offshore to the northwest (in a zone 150–300 km wide) is approximately parallel to the relative
motion between the Australian and Pacific plates. Hence, for that region, it is similar to the shear wave
splitting measurements reported here. Splitting from local S phases on both the MOANA OBSs and GeoNet
stations also suggest a possible lithospheric origin for the observed anisotropy (S. Karalliyadda, manuscript in
preparation, 2014).
Given these new shear wave splitting measurements and the available data on the characteristics of the mantle
under the South Island of New Zealand, it appears that either distributed lithospheric or asthenospheric
deformation is plausible. If anisotropy is the result of distributed deformation of the mantle lithosphere, we
expect a width of deformation around 4y0 = 100–140 km. If anisotropy is the result of localized lithospheric
deformation with pervasive shear in the asthenosphere, grain sizes on the order of 6–7 mm are required at
depths between 100 and 130 km below the lithosphere.
7. Conclusions
New shear wave splitting measurements made onshore and offshore the South Island of New Zealand show
an approximately 100–200 km wide zone of 1.0–2.0 s delay times with orientations of the fast quasi-shear
waves nearly parallel to the direction of relative motion between the Pacific and Australian plates. Regions of
distinctly different patterns of anisotropy bound this zone of high anisotropy. Approximately 300 km off the
west coast, little to no shear wave splitting is observed. Offshore the east coast, the anisotropy is clearly not a
result of simple shear between the Pacific and Australian plates and is consistent with its being due to current
absolute plate motion of the Pacific plate or frozen into the lithosphere.
We used these new shear wave splitting results to test two models of deformation to explain the observed
anisotropy: (1) a thin viscous sheet model mimicking distributed deformation in the mantle lithosphere and
(2) a model mimicking localized deformation in the mantle lithosphere around a fault that extends to the
asthenosphere, where deformation is then accommodated in a fan-like pattern centered beneath the fault. A
model of a thin viscous sheet with a width of deformation around 100–140 km could explain the observed
pattern of anisotropy. Likewise, if grain size at depths of 100–130 km into the asthenosphere were ~6–7 mm,
ZIETLOW ET AL.
©2013. American Geophysical Union. All Rights Reserved.
1038
Journal of Geophysical Research: Solid Earth
10.1002/2013JB010676
localized lithospheric deformation with diffuse shear in the underlying asthenosphere also fits our
measurements equally well. In any case, deformation in the upper mantle along this major shear zone in
the South Island of New Zealand appears confined to a 100–200 km wide region.
Acknowledgments
We thank Josh Stachnik and Zhaohui
Yang for their assistance in orienting the
horizontal components of the OBSs and
Megan Anderson for her help with the
SplitLab software. We also thank the
captain and crew of the R/V Thomas G.
Thompson (cruise TN229) in 2009 and of
the R/V Roger Revelle (cruise RR1002) in
2010. All 30 OBSs were manufactured by
Scripps Institution of Oceanography
and are part of the United States
National Ocean Bottom Seismograph
Instrumentation Pool. These data are
available for download from the IRIS
Data Management Center. We acknowledge the New Zealand GeoNet
project and its sponsors EQC, GNS
Science, and LINZ for also providing
data in this study. The figures were
made with the Generic Mapping
Tools (GMT) software by Wessel and Smith
[1998]. The (former) New Zealand
Foundation for Research, Science and
Technology, and the National Science
Foundation Continental Dynamics program supported this work under grants
EAR-0409564, EAR-0409609, and EAR0409835. We also thank Editor Tom
Parsons and two anonymous reviewers
for their constructive comments.
ZIETLOW ET AL.
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